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Analysis of daily clearness index, global and beam radiation for Beer Sheva, Israel: Partition according to day type and statistical analysis
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Energy Convers. Mgmt Vol. 37, No. 4, pp. 405416, 1996 Copyright © 1996 Elsevier Science Ltd 0196-8904(95)00193-X Printed in Great Britain. All rights reserved 0196-8904/96 $15.00+0.00
Pergamon
ANALYSIS OF DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION FOR BEER SHEVA, ISRAEL: PARTITION
ACCORDING STATISTICAL
TO DAY TYPE ANALYSIS
AND
A. I. K U D I S H 1 and A. IANETZ z LSolar Energy Laboratory, Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105 and 2Israel Meteorological Service, Research and Development Division, P.O. Box 25, Bet Dagan 50205, Israel
(Received 11 November 1994; received for pubfication 9 June 1995)
A~traet--The magnitude of the daily clearness index KT has been utilized to classify a day as either clear, partially cloudy or cloudy. The range of values for defining a day type was based upon a previous analysis of the Beer Sheva radiation database. These criteria were employed to partition the days according to type and the corresponding monthly average daily values for the clearness index, global, normal incidence and horizontal beam radiation were calculated. A statistical analysis was performed on each of the monthly average daily value subsets to help convey the shape of their respective distribution curves. The monthly average frequency of days according to type was also determined. Such an analysis of the solar radiation database for a particular site can be utilized to determine the relative merits of different types of solar energy conversion systems, e.g. concentrating vis-~.-vis non-concentrating solar collector systems. The results of this analysis for Beer Sheva indicate that this region is very amenable to the utilization of non-concentrating solar energy conversion systems, since the combined frequency of both clear and partially cloudy days exceeds 80% annually. In addition, the Beer Sheva region is a prime candidate for the use of solar energy conversion systems utilizing concentrating collectors due to its relatively high frequency of clear days and the fact that the monthly average daily values of the clearness index, even for partially cloudy days, are relatively high (KT > 0.50). Clearness index Cloudy days
Global radiation
Beam radiation
Clear days
Partially cloudy days
1. I N T R O D U C T I O N
The clearness index, for a particular time interval, is defined as the ratio of the global radiation to the extraterrestrial radiation. Thus, the daily clearness index KT is a measure of the fraction of the daily extraterrestrial solar radiation incident on a horizontal surface on the earth (the sum of the beam and diffuse) available for energy conversion. It is an integral measure of the amount and type of cloud cover, viz. it is an objective measure of the influence of cloud cover on the solar radiation flux as opposed to the subjective measure obtained via human observations. It also accounts for scattering caused by water vapor, air molecules and aerosols. The use of the clearness index to classify a particular time interval as clear, partially cloudy and cloudy has been reported in the literature (e.g. [1-4]). High values of the daily clearness index KT correspond to clear days, low values to cloudy days and intermediate values to partially cloudy days, Knowledge of the average values of the clearness index and the frequency of occurrence of different day types for a particular area can be very helpful in the design of solar energy conversion systems. In addition, clear days are characterized by relatively high fractions of the beam component in the horizontal global radiation. Consequently, sites possessing high clear day frequencies are most amenable to solar energy conversion systems utilizing concentrating devices, whereas the use of non-concentrating solar conversion systems would be recommended for sites characterized by high frequencies of partially cloudy days. We have utilized the daily clearness index to partition the days according to type and have calculated the corresponding monthly average daily global, normal incidence and horizontal beam 405
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
406
Table I. Geographical position of site, duration and source of data Site
Latitude
Longitude
Altitude (m MSL)
Climate
Duration of records
Reference
Beer Sheva
31°15' N
34°45' N
315
Semiarid
1982-93
5
radiation values for Beer Sheva, which is located in the southern Negev region of Israel, a semi-arid zone. A statistical analysis was performed on each of the monthly average daily value subsets. In addition, the monthly frequency of days according to type was determined. We believe that the analysis of the solar radiation database in such a manner can be very helpful in evaluating the relative merits of the different types of solar energy conversion systems, e.g. concentrating vis-fi-vis non-concentrating solar collector systems. 2. M E A S U R E M E N T S
In this study, daily global radiation data measured in Beer Sheva [5] are utilized to calculate the corresponding daily clearness index values. Site details and other pertinent information are listed in Table 1. The global radiation measurements were performed using an Eppley Precision Spectral Pyranometer, Model PSP, and the normal incidence radiation was measured using an Eppley Normal Incidence Pyrheliometer, Model NIP, and referred to solar time. This station is part of the national network of meteorological stations and the instrument calibration constants are checked at regular intervals by the Israel Meteorological Service. Each of these radiation-measuring instruments was initially connected to an electronic integrator and printer, but they are presently connected (since July 1988) to a rechargeable battery-powered datalogger (Campbell Scientific Instruments). The validity of the individual hourly values was checked in accordance with WMO recommendations [6]. Those values that did not comply with the WMO recommendations were considered erroneous and rejected (i.e. the corresponding daily value was rejected). As mentioned previously, the use of the daily clearness index to partition days according to types (clear, partially cloudy and cloudy) has been reported in the literature. In this analysis, the range of clearness index values corresponding to the three day types are defined based upon previous analysis of the Beer Sheva data [7], as follows: Clear days: KT > 0.65, Partially cloudy days: 0.35 < KT < 0.65, Cloudy days: KT < 0.35. The daily extraterrestrial radiation on a horizontal surface from sunrise to sunset H0, was calculated using the following equation: H0 = (24 x 3600G~/zt)[1 + 0.033 cos(360n/365)] x [cos ~b cos 6 cos ¢o~+ (2rrcoJ360)sin ~b sin 6],
(I)
where ~ is the site latitude, 6 is the solar declination angle, cos is the sunset hour angle, and Gsc is the solar constant (= 1367 W/m2). Table 2. Monthly average daily clearness index for Beer Sheva Month January February March April May June July August September October November December
Days
Average KT
Median Kr
Stdev KT
% CV
368 330 354 289 287 289 266 295 261 267 249 301
0.495 0.507 0.558 0.605 0.626 0.676 0.669 0.660 0.644 0.606 0.541 0.501
0.538 0.551 0.596 0.638 0.648 0.690 0.683 0.668 0.652 0.624 0.583 0.543
0.162 0.168 0.145 0.119 0.093 0.051 0.044 0.038 0.051 0.070 0.118 0.135
32.7 33.1 26.0 19.7 14.9 7.5 6.6 5.8 7.9 11.6 21.8 26.9
KUDISH and IANETZ: DALLY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION 100
-Beer
Sheva -----O---- % Clear - - e r a % Partially cloudy - - + - - % Cloudy
80
/I~
--
e
60 _-,,, ~
4o
20
o
t
I
I
I
,+"-~l
J
F
M
A
M
J
I
!
!
J
A
S
-, O
I
I
N
D
Month Fig. 1. Monthly frequency of occurrence of days according to type for Beer Sheva.
Table 3. Monthly average clearness index for clear, partially cloudy and cloudy days for Beer Sheva Month
Days
Average Kr
Median Kr
Stdev Kr
% CV
63 87 117 127 141 209 152 160 132 78 26 19
0.676 0.683 0.693 0.698 0.695 0.701 0.694 0.684 0.682 0.670 0.668 0.674
0.673 0.685 0.693 0.699 0.696 0.705 0.697 0.683 0.683 0.666 0.673
0.019 0.021 0.027 0.026 0.025 0.023 0.021 0.018 0.017 0.016 0.011
2.9 3.2 3.9 3.7 3.7 3.3 3.0 2.6 2.5 2.5 1.7
235 179 195 147 141 73 83 104 128 187 201 238
0.526 0.519 0.540 0.559 0.568 0.612 0.614 0.617 0.606 0.583 0.557 0.533
0.543 0.534 0.554 0.572 0.589 0.629 0.621 0.623 0.615 0.598 0.582 0.560
0.087 0.091 0.081 0.075 0.070 0.046 0.028 0.025 0.035 0.061 0.073 0.087
16.6 17.6 15.0 13.4 12.4 7.5 4.6 4.0 5.8 10.4 13.2 16.4
70 64 42 15 5 0 0 0 0 2 22 44
0.225 0.235 0.264 0.271 0.292
0.230 0.248 0.296
0.072 0.068 0.078
32.0 28.8 29.6
0.266 0.262
0.067 0.066
26.5 26.0
Clear days January February March April May June July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August September October November December
0.307 0.253 0.253
407
408
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
The measured hourly normal incidence beam radiation values Ib,n were converted to the beam radiation incident on a horizontal surface Ib, by applying the geometric conversion factor to the individual hourly values, viz. 56Ib = Ib,n COS0z, (2) where 0z is the average hourly incidence angle. These hourly values were, in turn, summed to determine the daily beam radiation incident on a horizontal surface Hb. 3. R E S U L T S
Clearness index
The monthly average daily clearness index values for Beer Sheva are reported in Table 2. Also listed in the table are the number of days in the individual monthly databases, the values for the median, standard deviation and percent coefficient of variation (% CV) for each month. The relative magnitude of the difference between the monthly median and average daily values is an indication of the degree of deviation of the corresponding daily clearness index distribution from a normal distribution. The % CV is defined as the ratio of the monthly standard deviation to the average daily values. It serves as an indication of the spread of the individual daily clearness index values about their average value (i.e. the broadness of the distribution curve). Table 4. Monthly average global radiation H for clear, partially cloudy and cloudy days for Beer Sheva Month
Days
Average H (MJ/m 2)
Median H (MJ/m 2)
Stdev H (MJ/m 2) % CV
63 88 117 128 141 209 152 163 132 78 26 19
14.11 17.38 21.95 25.71 27.86 28.92 28.17 25.99 22.71 18.36 14.87 13.00
14.05 17.33 22.20 25.68 27.91 29.06 28.24 25.92 22.72 18.58 14.94
0.88 1.16 1.57 1.24 1.04 0.95 0.95 1. I 1 1.26 1.34 0.81
6.3 6.7 7.1 4.8 3.7 3.3 3.4 4.3 5.5 7.3 5.5
233 178 196 146 137 73 76 100 122 187 158 238
10.84 13.10 16.83 20.52 22.78 25.22 25.14 23.36 20.23 15.90 12.29 I0.24
10.97 13.16 17.29 20.87 23.56 25.94 25.25 23.60 20.51 16.09 12.54 10.74
1.89 2.49 2.69 2.81 2.83 1.90 0.89 1.13 1.75 2.05 1.73 1.70
17.4 19.0 23.4 13.7 12.4 7.5 3.5 4.9 8.6 12.9 14.1 16.6
70 65 44 15 5 0 0 0 0 2 13 44
4.63 5.88 8.04 9.87 11.47
4.78 6.08 9.04
1.53 1.73 2.58
33.0 29.4 23.4
5.09
1.27
26.0
Clear days January February March April May June July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August September October November December
8.32 5.70 4.89
K U D I S H and IANETZ: D A I L Y C L E A R N E S S INDEX, G L O B A L A N D BEAM R A D I A T I O N
409
It can be observed from the corresponding monthly median and average daily values reported in Table 2 that the former is greater than the latter throughout the year. This indicates that more than half of the daily values in the individual monthly databases are greater than the average value. Nevertheless, the distribution of the daily clearness index values for the months of June through September approach a normal distribution (viz. the percent deviation between the median and average values is between 1.2 and 2.1%). In addition, the % CV values for these months are relatively low (between 5.8% and 7.9% ), evidence of a narrow distribution curve. The latter is, in essence, an indication of the relative stability of the solar radiation conditions during these months. The results of the individual monthly frequency analysis of the days according to type, based upon the criteria mentioned above, are shown in Fig. 1 as the percentage of days that are of a particular type during each month. It is observed that there are no days classified as cloudy for the months of June through September, although there are a relatively small number of cloudy hours, occurring before 9:00 and after 16:00, during these months. In fact, throughout the year, the monthly average of cloudy days does not exceed 20%. On the other hand, the monthly average of clear days drops below 20% for only four months (viz. January, February, November and December). The statistical analysis of the monthly average daily clearness index values, partitioned according to day type, are reported in Table 3. If the number of days in an individual monthly day type Table 5. Monthly average normal incidence beam radiation nb,n for clear, partially cloudy and cloudy days for Beer Sheva Average Hb,n Median Hb,n Month
Stdev Hb,n
Days
(MJ/m 2)
(MJ/m 2)
(MJ/m 2)
% CV
33 52 75 104 118 138 144 106 109 50 18 5
21.84 23.80 23.93 25.69 26.59 29.11 28.27 26.50 24.70 22.49 22.26 20.86
21.99 24.05 24.46 25.75 26.92 29.24 28.42 26.66 25.10 22.35
3.01 3.13 4.60 4.38 4.40 3.83 3.46 3.19 3.41 2.72
13.8 13.2 19.2 17.1 16.5 13.0 12.2 12.0 13.8 12.1
143 112 127 82 78 12 17 22 36 84 118 104
11.67 12.10 12.58 14.17 15.18 17.15 21.69 19.68 17.48 15.79 14.17 I 1.49
11.13 11.87 11.93 14.88 15.07
5.93 6.05 6.26 5.05 6.26
50.8 50.0 49.8 35.6 41.2
20.40 18.56 16.54 15.76 12.48
4.10 3.90 4.08 5.23 5.46
20.8 22.3 25.9 36.9 47.6
43 37 23 I0 5 0 0 0 0 0 8 32
1.06 1.15 1.86 1.96 1.92
0.65 0.82 1.65
I. 14 0.99 1.68
107.9 86. I 90.1
0.90
3.25
135.7
Clear days January February March April May June
July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August
September October November December ECM 37/4~C
2.06 2.39
410
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
database was less than 20, no statistical analysis was performed, and just the average value was reported. It is observed that, in the case of clear days, the corresponding median and average values differ by less than 1% and the % CV values do not exceed 4% throughout the year. (December was excluded from the analysis due to the lack of the minimum number of clear days.) Thus, the individual monthly distributions of the subset clear days can be described as approaching a relatively narrow, normal distribution. In fact, one may say that, in the case of Beer Sheva, "one clear day is like another". The results of the statistical analysis of the partially cloudy day monthly subsets are similar to those for the monthly average daily clearness index values, viz. the median is greater than the corresponding average value throughout the year and the % CV values for June through September are relatively low. The fact that the deviation between the median and average values and the magnitude of the % CV are lower than those in the corresponding original (unpartitioned) monthly databases is simply a consequence of the narrower range of values included in the subsets. The statistical analysis of the cloudy day monthly subsets is limited to only five months (see Table 3) due to the small number of cloudy days occurring from April through October, and this is the significant finding from the energy conversion aspect. The magnitude of the % CV is a reflection of the relatively small values comprising these subsets, i.e. the standard deviations are
Table 6. Monthly average horizontal beam radiation Hb,n for clear, partially cloudy and cloudy days for Beer Sheva Month
Days
Average Hb,. (MJ/m 2)
Median Hb,. (MJ/m 2)
Stdev Hb.n (MJ/m 2) % CV
33 52 75 104 118 138 144 106 109 50 18 5
10.32 12.91 15.42 18.19 19.74 21.66 21.06 19.43 16.34 12.99 10.94 9.20
10.40 13.27 16.05 18.24 19.56 21.92 21.27 19.53 16.73 13.03
1.37 1.82 2.85 2.65 2.86 2.41 2.23 2.06 2.42 1.41
13.3 14.0 18.0 14.6 14.5 11.1 10.6 10.6 14.8 10.8
143 112 127 82 78 12 17 22 36 84 118 104
5.40 6.53 7.97 10.06 11.33 12.66 16.11 14.61 11.92 9.18 7.60 5.46
5.13 6.29 7.57 10.34 11.25
2.72 3.34 4.00 3.52 4.61
50.0 51.0 50.0 35.0 40.1
15.19 12.50 9.77 8.47 5.73
2.77 2.85 2.62 2.81 2.55
18.9 23.9 28.6 36.9 46.7
43 37 23 10 5 0 0 0 0 0 8 32
0.47 0.60 1.09 1.25 1.39
0.26 0.37 0.84
0.50 0.53 1.02
105.0 88.2 93.5
0.43
1.32
132.5
Clear days January February March April May June July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August September October November December
1.02 1.00
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
411
I Global radiation
40I
+J
/
./.
-
+ / + ~ + ~ +
uear.ay
N~xtraterrestrial
Average daily ,
",*~X+ I
20--
10--
,,
0 J
F
M
A
M
J
J
A
S
O
N
D
Month Fig. 2. Monthly average daily global radiation according to type for Beer Sheva.
of the same order of magnitude, but the average values are less than half of the corresponding values in the partially cloudy subsets. Solar radiation
The results of the partition of the daily global, normal incidence and horizontal beam radiation values on the basis of the corresponding KT values (viz. the criteria for classifying day type) are reported in Tables 4-6. The discrepancy between the number of days in the corresponding individual monthly databases between KT, global and beam radiation is a result of the fact that the three databases were not identical. The same general comments apply to Tables 4-6 as were mentioned previously regarding Table 3. We will outline, in the following section, how these results can be utilized to analyze the relative merits of different types of solar energy conversion systems, e.g. concentrating vis-~t-vis non-concentrating solar collector systems, for this region. Nip radiation 40--
Clear day 30--
2o
,
C
I0
e""-e
Partially cloudy day
~o
C l o u d y day
J
F
M
A
M
J
J
A
S
0
N
D
Month Fig. 3. Monthly average daily normal incidence radiation according to type for Beer Sheva.
412
KUDISH and IANETZ:DAILYCLEARNESSINDEX,GLOBALAND BEAMRADIATION Beam radiation
1
~/+--.--+~
40 ~-
/ ~
[
~
/
~ 30 -
.s+
Extraterrestrial
+\,1 +
Clearday [
N 20 +
~ 10 - - - - ~ ~ O P/arti~ll~~c ~ e.~e Cloudyday
~
o
J
F
M
A
M
J
J
A
S
O
N
D
Month Fig. 4. Monthlyaveragedailyhorizontalbeamradiationaccordingto type for BeerSheva.
The monthly average daily global, normal incidence and horizontal beam radiation values together with their corresponding average values according to day type and the extraterrestrial radiation on a horizontal surface are plotted in Figs 2-4, respectively. This facilitates a visual comparison of the five parameters and enables one to approximate, for a particular month, the type of day closely approaching the average day. We have also presented in Figs 5-6 the average hourly global radiation values and average hourly frequency according to day type for four months, each being representative of a particular season. In all four cases, hours classified as clear and/or partially cloudy dominate the midday hours from l0: 00 to 14: 00. It should also be noted that the major portion of the daily solar radiation is incident
(a) 3000January
20000 .~,
"~
\ 1000 --
0
I
I
I
I
I
I
8
10
12
14
16
18
Hour
Fig. 5(a)--caption
opposite.
©
-eP.
0
m
0
6"
o
-
f
~
_./~
o
Global radiation (kJ/m 2)
I
O
~
X-
F
70-
O
,/'/
'
°
Global radiation (kJ/m 2) g I
o
,.e
-
oo -
/ _.~/-
/.~~
+/"
+\+~~"'~
.~.~
oo
L'f
../2--7
g
Global radiation (kJ/m 2)
I
g >
I
o o o
lO0-(a)
January
80
=
0
..\
60
"\ ~ ~, 40
/\
~d
-+,, J~>-~t-
i;
20
__1 10
8
12
14
16
18
14
16
18
Hour (b)
100 I April
8o[•~ 60
0 8
40
8
10
12 Hour
(c)
1oo
July
~
/•
Q 60 ~D 40
o
6
8
I0
12
14
Hour Figs
6(a)-(c)--caption opposite.
IL ~
16
18
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
(d)
415
100 -- October
8o = o
.
J\
60
0
,
8
10
]
12
14
16
18
Hour Fig. 6. Monthly average frequency of occurrence of hours according to type for Beer Sheva: (C)) clear hour: (Q) partially cloudy hour: (+) cloudy hour.
during this time interval. The two sets of data corresponding to a single month should be considered complementary, since the magnitude and frequency of occurrence complement each other with regard to energy conversion potential (viz. availability and magnitude). 4. DISCUSSION It is apparent from the analysis of the daily clearness index values that Beer Sheva and the northern Negev region are prime candidates for solar energy conversion systems. On an average annual basis, more than 80% of the days are classified as either clear or partially cloudy, viz. less than 20% of the days are defined as cloudy. In fact, the individual monthly average percentage of cloudy days exceeds 10% for only four months (January, February, March and December) during the year. On the other hand, the individual monthly average percentage of clear days drops below 20% for only three months (January, November and December). In addition, the average monthly Kx value exceeds 0.60 from April through October (see Table 2). In general, the global radiation on clear days is characterized by a relatively high fraction of beam radiation. It is observed from the data shown in Fig. 1 that the monthly average percentage of clear days exceeds 50% from June through September. In fact, during this interval, it is observed that no days were classified as cloudy and also that the monthly average KT exceeds 0.60 even for the days classified as partially cloudy. Thus, the solar energy resource available during this time interval in this region is considerable. The question is not whether to utilize the abundant solar energy available but what type of solar energy conversion system is preferable. As mentioned previously, it is possible to utilize Tables 4-6 to analyze the relative merits of solar energy conversion by means of concentrating vis-fi-vis non-concentrating solar collector systems. First of all, the monthly average frequency of days according to type gives an initial indication of the relative viability of different solar collector types. Concentrating solar collectors operate best under clear day conditions and, to a much lesser extent, under partially cloudy days. The major difference between day types is the significant reduction in the beam radiation available for energy conversion for the latter. In the case or Beer Sheva, the monthly average daily beam radiation available for energy conversion on partially cloudy days is reduced by a factor ranging from 0.51 to 0.71 relative to that available on clear days (see Table 5). On the other hand, the global radiation, utilized for energy conversion by non-concentrating solar collectors, available on partially cloudy days does not differ significantly from that on clear days. It is reduced by a factor ranging from 0.77 to 0.90 (see Table 4). The monthly average fraction of cloudy
416
KUDISHand IANETZ: DAILY CLEARNESS INDEX, GLOBALAND BEAM RADIATION
days defines the down-time (viz. the time of negligible or no energy production) for both system types. A comprehensive simulation of the relative annual performance of the two different system types can be executed utilizing the results of the partition analysis based upon the clearness index data. The average annual productivity of a solar conversion system would be simulated by an appropriate model utilizing the radiation data reported in the tables in conjunction with the solar collector system parameters (optical and thermal). In the case of a non-concentrating solar collector system, the monthly average daily global radiation values according to day type, corrected for collector azimuth and tilt angles (preferably utilizing the horizontal beam and diffuse radiation components, the latter calculated as the difference between the global and horizontal beam radiation, to perform this correction) and weighted by the frequency factor (i.e. the fraction of days per month of a particular type), would be the energy input. In the case of a concentrating system, the monthly average daily normal incidence radiation values according to day type weighted by the frequency factor would be the energy input in the case of a 2-axis tracking system. (A geometric correction factor would be applied in the case of other types of concentrating systems.) Once the average annual productivity for each system is determined, the next stage would be to perform an appropriate economic analysis utilizing the costs associated with each system. The simulation model, of course, does not have to be limited to the solar collector loop, but may also include other components of the overall system (such as the storage loop). 5. C O N C L U S I O N S The main conclusions from this analysis of the daily clearness index and radiation data in conjunction with the partition according to day type for Beer Sheva are the following: (1) This region is characterized by a relatively low percentage of cloudy days. Only for four months during the year does the monthly average percentage of cloudy days exceed 10%. Since the monthly average frequency of clear and partially cloudy days for Beer Sheva exceeds 80% throughout the year, this region is unequivocally amenable to the utilization of non-concentrating solar energy conversion systems. (2) There are no days classified as cloudy during the months of June through September and the monthly average percentage of clear days exceeds 50% during these months. Thus, the Beer Sheva region is a prime candidate for the use of solar energy conversion systems utilizing concentrating collectors due to its relatively high frequency of clear days and the fact that the monthly average daily values of the clearness index, even for partially cloudy days, are relatively high (KT > 0.50). (3) A general procedure has been outlined for utilizing the partition of days according to type analysis of the radiation data to analyze the relative merits of solar energy conversion by means of concentrating vis-fi-vis non-concentrating solar collector systems. Acknowledgements--We are indebted to E. Berman for partial support of this research by funding the purchase of the Normal IncidencePyrheliometersystem.We wish to thank G. Stanhillof the VolcaniInstitutefor remarks and suggestions during the preparation of this manuscript.We also wishto thank A. Manesand I. Seterof the Israel MeteorologicalService for their encouragementof this joint research project. REFERENCES
1. J. F. Orgill and K. G. T. Hollands, Sol. Energy 19, 357 (1977). 2. M. Iqbal, Sol. Energy 24, 491 (1980). 3. D. G. Erbs, S. A. Klein and J. A. Duffle,Sol. Energy 28, 293 (1982). 4. M. A. Chendo and A. A. L. Maduekwe,Sol. Energy 52, 247 (1994). 5. A. I. Kudish and A. Ianetz, Sol. Energy 48, 97 (1992). 6. World MeteorologicalOrganization, World Climate Program Report WCP-48 (1983). 7. A. Ianetz and A. I. Kudish, Energy 17, 523 (1992).
Energy Convers. Mgmt Vol. 37, No. 4, pp. 405416, 1996 Copyright © 1996 Elsevier Science Ltd 0196-8904(95)00193-X Printed in Great Britain. All rights reserved 0196-8904/96 $15.00+0.00
Pergamon
ANALYSIS OF DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION FOR BEER SHEVA, ISRAEL: PARTITION
ACCORDING STATISTICAL
TO DAY TYPE ANALYSIS
AND
A. I. K U D I S H 1 and A. IANETZ z LSolar Energy Laboratory, Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105 and 2Israel Meteorological Service, Research and Development Division, P.O. Box 25, Bet Dagan 50205, Israel
(Received 11 November 1994; received for pubfication 9 June 1995)
A~traet--The magnitude of the daily clearness index KT has been utilized to classify a day as either clear, partially cloudy or cloudy. The range of values for defining a day type was based upon a previous analysis of the Beer Sheva radiation database. These criteria were employed to partition the days according to type and the corresponding monthly average daily values for the clearness index, global, normal incidence and horizontal beam radiation were calculated. A statistical analysis was performed on each of the monthly average daily value subsets to help convey the shape of their respective distribution curves. The monthly average frequency of days according to type was also determined. Such an analysis of the solar radiation database for a particular site can be utilized to determine the relative merits of different types of solar energy conversion systems, e.g. concentrating vis-~.-vis non-concentrating solar collector systems. The results of this analysis for Beer Sheva indicate that this region is very amenable to the utilization of non-concentrating solar energy conversion systems, since the combined frequency of both clear and partially cloudy days exceeds 80% annually. In addition, the Beer Sheva region is a prime candidate for the use of solar energy conversion systems utilizing concentrating collectors due to its relatively high frequency of clear days and the fact that the monthly average daily values of the clearness index, even for partially cloudy days, are relatively high (KT > 0.50). Clearness index Cloudy days
Global radiation
Beam radiation
Clear days
Partially cloudy days
1. I N T R O D U C T I O N
The clearness index, for a particular time interval, is defined as the ratio of the global radiation to the extraterrestrial radiation. Thus, the daily clearness index KT is a measure of the fraction of the daily extraterrestrial solar radiation incident on a horizontal surface on the earth (the sum of the beam and diffuse) available for energy conversion. It is an integral measure of the amount and type of cloud cover, viz. it is an objective measure of the influence of cloud cover on the solar radiation flux as opposed to the subjective measure obtained via human observations. It also accounts for scattering caused by water vapor, air molecules and aerosols. The use of the clearness index to classify a particular time interval as clear, partially cloudy and cloudy has been reported in the literature (e.g. [1-4]). High values of the daily clearness index KT correspond to clear days, low values to cloudy days and intermediate values to partially cloudy days, Knowledge of the average values of the clearness index and the frequency of occurrence of different day types for a particular area can be very helpful in the design of solar energy conversion systems. In addition, clear days are characterized by relatively high fractions of the beam component in the horizontal global radiation. Consequently, sites possessing high clear day frequencies are most amenable to solar energy conversion systems utilizing concentrating devices, whereas the use of non-concentrating solar conversion systems would be recommended for sites characterized by high frequencies of partially cloudy days. We have utilized the daily clearness index to partition the days according to type and have calculated the corresponding monthly average daily global, normal incidence and horizontal beam 405
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
406
Table I. Geographical position of site, duration and source of data Site
Latitude
Longitude
Altitude (m MSL)
Climate
Duration of records
Reference
Beer Sheva
31°15' N
34°45' N
315
Semiarid
1982-93
5
radiation values for Beer Sheva, which is located in the southern Negev region of Israel, a semi-arid zone. A statistical analysis was performed on each of the monthly average daily value subsets. In addition, the monthly frequency of days according to type was determined. We believe that the analysis of the solar radiation database in such a manner can be very helpful in evaluating the relative merits of the different types of solar energy conversion systems, e.g. concentrating vis-fi-vis non-concentrating solar collector systems. 2. M E A S U R E M E N T S
In this study, daily global radiation data measured in Beer Sheva [5] are utilized to calculate the corresponding daily clearness index values. Site details and other pertinent information are listed in Table 1. The global radiation measurements were performed using an Eppley Precision Spectral Pyranometer, Model PSP, and the normal incidence radiation was measured using an Eppley Normal Incidence Pyrheliometer, Model NIP, and referred to solar time. This station is part of the national network of meteorological stations and the instrument calibration constants are checked at regular intervals by the Israel Meteorological Service. Each of these radiation-measuring instruments was initially connected to an electronic integrator and printer, but they are presently connected (since July 1988) to a rechargeable battery-powered datalogger (Campbell Scientific Instruments). The validity of the individual hourly values was checked in accordance with WMO recommendations [6]. Those values that did not comply with the WMO recommendations were considered erroneous and rejected (i.e. the corresponding daily value was rejected). As mentioned previously, the use of the daily clearness index to partition days according to types (clear, partially cloudy and cloudy) has been reported in the literature. In this analysis, the range of clearness index values corresponding to the three day types are defined based upon previous analysis of the Beer Sheva data [7], as follows: Clear days: KT > 0.65, Partially cloudy days: 0.35 < KT < 0.65, Cloudy days: KT < 0.35. The daily extraterrestrial radiation on a horizontal surface from sunrise to sunset H0, was calculated using the following equation: H0 = (24 x 3600G~/zt)[1 + 0.033 cos(360n/365)] x [cos ~b cos 6 cos ¢o~+ (2rrcoJ360)sin ~b sin 6],
(I)
where ~ is the site latitude, 6 is the solar declination angle, cos is the sunset hour angle, and Gsc is the solar constant (= 1367 W/m2). Table 2. Monthly average daily clearness index for Beer Sheva Month January February March April May June July August September October November December
Days
Average KT
Median Kr
Stdev KT
% CV
368 330 354 289 287 289 266 295 261 267 249 301
0.495 0.507 0.558 0.605 0.626 0.676 0.669 0.660 0.644 0.606 0.541 0.501
0.538 0.551 0.596 0.638 0.648 0.690 0.683 0.668 0.652 0.624 0.583 0.543
0.162 0.168 0.145 0.119 0.093 0.051 0.044 0.038 0.051 0.070 0.118 0.135
32.7 33.1 26.0 19.7 14.9 7.5 6.6 5.8 7.9 11.6 21.8 26.9
KUDISH and IANETZ: DALLY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION 100
-Beer
Sheva -----O---- % Clear - - e r a % Partially cloudy - - + - - % Cloudy
80
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Month Fig. 1. Monthly frequency of occurrence of days according to type for Beer Sheva.
Table 3. Monthly average clearness index for clear, partially cloudy and cloudy days for Beer Sheva Month
Days
Average Kr
Median Kr
Stdev Kr
% CV
63 87 117 127 141 209 152 160 132 78 26 19
0.676 0.683 0.693 0.698 0.695 0.701 0.694 0.684 0.682 0.670 0.668 0.674
0.673 0.685 0.693 0.699 0.696 0.705 0.697 0.683 0.683 0.666 0.673
0.019 0.021 0.027 0.026 0.025 0.023 0.021 0.018 0.017 0.016 0.011
2.9 3.2 3.9 3.7 3.7 3.3 3.0 2.6 2.5 2.5 1.7
235 179 195 147 141 73 83 104 128 187 201 238
0.526 0.519 0.540 0.559 0.568 0.612 0.614 0.617 0.606 0.583 0.557 0.533
0.543 0.534 0.554 0.572 0.589 0.629 0.621 0.623 0.615 0.598 0.582 0.560
0.087 0.091 0.081 0.075 0.070 0.046 0.028 0.025 0.035 0.061 0.073 0.087
16.6 17.6 15.0 13.4 12.4 7.5 4.6 4.0 5.8 10.4 13.2 16.4
70 64 42 15 5 0 0 0 0 2 22 44
0.225 0.235 0.264 0.271 0.292
0.230 0.248 0.296
0.072 0.068 0.078
32.0 28.8 29.6
0.266 0.262
0.067 0.066
26.5 26.0
Clear days January February March April May June July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August September October November December
0.307 0.253 0.253
407
408
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
The measured hourly normal incidence beam radiation values Ib,n were converted to the beam radiation incident on a horizontal surface Ib, by applying the geometric conversion factor to the individual hourly values, viz. 56Ib = Ib,n COS0z, (2) where 0z is the average hourly incidence angle. These hourly values were, in turn, summed to determine the daily beam radiation incident on a horizontal surface Hb. 3. R E S U L T S
Clearness index
The monthly average daily clearness index values for Beer Sheva are reported in Table 2. Also listed in the table are the number of days in the individual monthly databases, the values for the median, standard deviation and percent coefficient of variation (% CV) for each month. The relative magnitude of the difference between the monthly median and average daily values is an indication of the degree of deviation of the corresponding daily clearness index distribution from a normal distribution. The % CV is defined as the ratio of the monthly standard deviation to the average daily values. It serves as an indication of the spread of the individual daily clearness index values about their average value (i.e. the broadness of the distribution curve). Table 4. Monthly average global radiation H for clear, partially cloudy and cloudy days for Beer Sheva Month
Days
Average H (MJ/m 2)
Median H (MJ/m 2)
Stdev H (MJ/m 2) % CV
63 88 117 128 141 209 152 163 132 78 26 19
14.11 17.38 21.95 25.71 27.86 28.92 28.17 25.99 22.71 18.36 14.87 13.00
14.05 17.33 22.20 25.68 27.91 29.06 28.24 25.92 22.72 18.58 14.94
0.88 1.16 1.57 1.24 1.04 0.95 0.95 1. I 1 1.26 1.34 0.81
6.3 6.7 7.1 4.8 3.7 3.3 3.4 4.3 5.5 7.3 5.5
233 178 196 146 137 73 76 100 122 187 158 238
10.84 13.10 16.83 20.52 22.78 25.22 25.14 23.36 20.23 15.90 12.29 I0.24
10.97 13.16 17.29 20.87 23.56 25.94 25.25 23.60 20.51 16.09 12.54 10.74
1.89 2.49 2.69 2.81 2.83 1.90 0.89 1.13 1.75 2.05 1.73 1.70
17.4 19.0 23.4 13.7 12.4 7.5 3.5 4.9 8.6 12.9 14.1 16.6
70 65 44 15 5 0 0 0 0 2 13 44
4.63 5.88 8.04 9.87 11.47
4.78 6.08 9.04
1.53 1.73 2.58
33.0 29.4 23.4
5.09
1.27
26.0
Clear days January February March April May June July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August September October November December
8.32 5.70 4.89
K U D I S H and IANETZ: D A I L Y C L E A R N E S S INDEX, G L O B A L A N D BEAM R A D I A T I O N
409
It can be observed from the corresponding monthly median and average daily values reported in Table 2 that the former is greater than the latter throughout the year. This indicates that more than half of the daily values in the individual monthly databases are greater than the average value. Nevertheless, the distribution of the daily clearness index values for the months of June through September approach a normal distribution (viz. the percent deviation between the median and average values is between 1.2 and 2.1%). In addition, the % CV values for these months are relatively low (between 5.8% and 7.9% ), evidence of a narrow distribution curve. The latter is, in essence, an indication of the relative stability of the solar radiation conditions during these months. The results of the individual monthly frequency analysis of the days according to type, based upon the criteria mentioned above, are shown in Fig. 1 as the percentage of days that are of a particular type during each month. It is observed that there are no days classified as cloudy for the months of June through September, although there are a relatively small number of cloudy hours, occurring before 9:00 and after 16:00, during these months. In fact, throughout the year, the monthly average of cloudy days does not exceed 20%. On the other hand, the monthly average of clear days drops below 20% for only four months (viz. January, February, November and December). The statistical analysis of the monthly average daily clearness index values, partitioned according to day type, are reported in Table 3. If the number of days in an individual monthly day type Table 5. Monthly average normal incidence beam radiation nb,n for clear, partially cloudy and cloudy days for Beer Sheva Average Hb,n Median Hb,n Month
Stdev Hb,n
Days
(MJ/m 2)
(MJ/m 2)
(MJ/m 2)
% CV
33 52 75 104 118 138 144 106 109 50 18 5
21.84 23.80 23.93 25.69 26.59 29.11 28.27 26.50 24.70 22.49 22.26 20.86
21.99 24.05 24.46 25.75 26.92 29.24 28.42 26.66 25.10 22.35
3.01 3.13 4.60 4.38 4.40 3.83 3.46 3.19 3.41 2.72
13.8 13.2 19.2 17.1 16.5 13.0 12.2 12.0 13.8 12.1
143 112 127 82 78 12 17 22 36 84 118 104
11.67 12.10 12.58 14.17 15.18 17.15 21.69 19.68 17.48 15.79 14.17 I 1.49
11.13 11.87 11.93 14.88 15.07
5.93 6.05 6.26 5.05 6.26
50.8 50.0 49.8 35.6 41.2
20.40 18.56 16.54 15.76 12.48
4.10 3.90 4.08 5.23 5.46
20.8 22.3 25.9 36.9 47.6
43 37 23 I0 5 0 0 0 0 0 8 32
1.06 1.15 1.86 1.96 1.92
0.65 0.82 1.65
I. 14 0.99 1.68
107.9 86. I 90.1
0.90
3.25
135.7
Clear days January February March April May June
July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August
September October November December ECM 37/4~C
2.06 2.39
410
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
database was less than 20, no statistical analysis was performed, and just the average value was reported. It is observed that, in the case of clear days, the corresponding median and average values differ by less than 1% and the % CV values do not exceed 4% throughout the year. (December was excluded from the analysis due to the lack of the minimum number of clear days.) Thus, the individual monthly distributions of the subset clear days can be described as approaching a relatively narrow, normal distribution. In fact, one may say that, in the case of Beer Sheva, "one clear day is like another". The results of the statistical analysis of the partially cloudy day monthly subsets are similar to those for the monthly average daily clearness index values, viz. the median is greater than the corresponding average value throughout the year and the % CV values for June through September are relatively low. The fact that the deviation between the median and average values and the magnitude of the % CV are lower than those in the corresponding original (unpartitioned) monthly databases is simply a consequence of the narrower range of values included in the subsets. The statistical analysis of the cloudy day monthly subsets is limited to only five months (see Table 3) due to the small number of cloudy days occurring from April through October, and this is the significant finding from the energy conversion aspect. The magnitude of the % CV is a reflection of the relatively small values comprising these subsets, i.e. the standard deviations are
Table 6. Monthly average horizontal beam radiation Hb,n for clear, partially cloudy and cloudy days for Beer Sheva Month
Days
Average Hb,. (MJ/m 2)
Median Hb,. (MJ/m 2)
Stdev Hb.n (MJ/m 2) % CV
33 52 75 104 118 138 144 106 109 50 18 5
10.32 12.91 15.42 18.19 19.74 21.66 21.06 19.43 16.34 12.99 10.94 9.20
10.40 13.27 16.05 18.24 19.56 21.92 21.27 19.53 16.73 13.03
1.37 1.82 2.85 2.65 2.86 2.41 2.23 2.06 2.42 1.41
13.3 14.0 18.0 14.6 14.5 11.1 10.6 10.6 14.8 10.8
143 112 127 82 78 12 17 22 36 84 118 104
5.40 6.53 7.97 10.06 11.33 12.66 16.11 14.61 11.92 9.18 7.60 5.46
5.13 6.29 7.57 10.34 11.25
2.72 3.34 4.00 3.52 4.61
50.0 51.0 50.0 35.0 40.1
15.19 12.50 9.77 8.47 5.73
2.77 2.85 2.62 2.81 2.55
18.9 23.9 28.6 36.9 46.7
43 37 23 10 5 0 0 0 0 0 8 32
0.47 0.60 1.09 1.25 1.39
0.26 0.37 0.84
0.50 0.53 1.02
105.0 88.2 93.5
0.43
1.32
132.5
Clear days January February March April May June July August September October November December
Partially cloudy days January February March April May June July August September October November December
Cloudy days January February March April May June July August September October November December
1.02 1.00
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
411
I Global radiation
40I
+J
/
./.
-
+ / + ~ + ~ +
uear.ay
N~xtraterrestrial
Average daily ,
",*~X+ I
20--
10--
,,
0 J
F
M
A
M
J
J
A
S
O
N
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Month Fig. 2. Monthly average daily global radiation according to type for Beer Sheva.
of the same order of magnitude, but the average values are less than half of the corresponding values in the partially cloudy subsets. Solar radiation
The results of the partition of the daily global, normal incidence and horizontal beam radiation values on the basis of the corresponding KT values (viz. the criteria for classifying day type) are reported in Tables 4-6. The discrepancy between the number of days in the corresponding individual monthly databases between KT, global and beam radiation is a result of the fact that the three databases were not identical. The same general comments apply to Tables 4-6 as were mentioned previously regarding Table 3. We will outline, in the following section, how these results can be utilized to analyze the relative merits of different types of solar energy conversion systems, e.g. concentrating vis-~t-vis non-concentrating solar collector systems, for this region. Nip radiation 40--
Clear day 30--
2o
,
C
I0
e""-e
Partially cloudy day
~o
C l o u d y day
J
F
M
A
M
J
J
A
S
0
N
D
Month Fig. 3. Monthly average daily normal incidence radiation according to type for Beer Sheva.
412
KUDISH and IANETZ:DAILYCLEARNESSINDEX,GLOBALAND BEAMRADIATION Beam radiation
1
~/+--.--+~
40 ~-
/ ~
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+\,1 +
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~
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Month Fig. 4. Monthlyaveragedailyhorizontalbeamradiationaccordingto type for BeerSheva.
The monthly average daily global, normal incidence and horizontal beam radiation values together with their corresponding average values according to day type and the extraterrestrial radiation on a horizontal surface are plotted in Figs 2-4, respectively. This facilitates a visual comparison of the five parameters and enables one to approximate, for a particular month, the type of day closely approaching the average day. We have also presented in Figs 5-6 the average hourly global radiation values and average hourly frequency according to day type for four months, each being representative of a particular season. In all four cases, hours classified as clear and/or partially cloudy dominate the midday hours from l0: 00 to 14: 00. It should also be noted that the major portion of the daily solar radiation is incident
(a) 3000January
20000 .~,
"~
\ 1000 --
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8
10
12
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Fig. 5(a)--caption
opposite.
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o
-
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o
Global radiation (kJ/m 2)
I
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o
,.e
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lO0-(a)
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=
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/\
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-+,, J~>-~t-
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12
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16
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100 I April
8o[•~ 60
0 8
40
8
10
12 Hour
(c)
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o
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IL ~
16
18
KUDISH and IANETZ: DAILY CLEARNESS INDEX, GLOBAL AND BEAM RADIATION
(d)
415
100 -- October
8o = o
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60
0
,
8
10
]
12
14
16
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Hour Fig. 6. Monthly average frequency of occurrence of hours according to type for Beer Sheva: (C)) clear hour: (Q) partially cloudy hour: (+) cloudy hour.
during this time interval. The two sets of data corresponding to a single month should be considered complementary, since the magnitude and frequency of occurrence complement each other with regard to energy conversion potential (viz. availability and magnitude). 4. DISCUSSION It is apparent from the analysis of the daily clearness index values that Beer Sheva and the northern Negev region are prime candidates for solar energy conversion systems. On an average annual basis, more than 80% of the days are classified as either clear or partially cloudy, viz. less than 20% of the days are defined as cloudy. In fact, the individual monthly average percentage of cloudy days exceeds 10% for only four months (January, February, March and December) during the year. On the other hand, the individual monthly average percentage of clear days drops below 20% for only three months (January, November and December). In addition, the average monthly Kx value exceeds 0.60 from April through October (see Table 2). In general, the global radiation on clear days is characterized by a relatively high fraction of beam radiation. It is observed from the data shown in Fig. 1 that the monthly average percentage of clear days exceeds 50% from June through September. In fact, during this interval, it is observed that no days were classified as cloudy and also that the monthly average KT exceeds 0.60 even for the days classified as partially cloudy. Thus, the solar energy resource available during this time interval in this region is considerable. The question is not whether to utilize the abundant solar energy available but what type of solar energy conversion system is preferable. As mentioned previously, it is possible to utilize Tables 4-6 to analyze the relative merits of solar energy conversion by means of concentrating vis-fi-vis non-concentrating solar collector systems. First of all, the monthly average frequency of days according to type gives an initial indication of the relative viability of different solar collector types. Concentrating solar collectors operate best under clear day conditions and, to a much lesser extent, under partially cloudy days. The major difference between day types is the significant reduction in the beam radiation available for energy conversion for the latter. In the case or Beer Sheva, the monthly average daily beam radiation available for energy conversion on partially cloudy days is reduced by a factor ranging from 0.51 to 0.71 relative to that available on clear days (see Table 5). On the other hand, the global radiation, utilized for energy conversion by non-concentrating solar collectors, available on partially cloudy days does not differ significantly from that on clear days. It is reduced by a factor ranging from 0.77 to 0.90 (see Table 4). The monthly average fraction of cloudy
416
KUDISHand IANETZ: DAILY CLEARNESS INDEX, GLOBALAND BEAM RADIATION
days defines the down-time (viz. the time of negligible or no energy production) for both system types. A comprehensive simulation of the relative annual performance of the two different system types can be executed utilizing the results of the partition analysis based upon the clearness index data. The average annual productivity of a solar conversion system would be simulated by an appropriate model utilizing the radiation data reported in the tables in conjunction with the solar collector system parameters (optical and thermal). In the case of a non-concentrating solar collector system, the monthly average daily global radiation values according to day type, corrected for collector azimuth and tilt angles (preferably utilizing the horizontal beam and diffuse radiation components, the latter calculated as the difference between the global and horizontal beam radiation, to perform this correction) and weighted by the frequency factor (i.e. the fraction of days per month of a particular type), would be the energy input. In the case of a concentrating system, the monthly average daily normal incidence radiation values according to day type weighted by the frequency factor would be the energy input in the case of a 2-axis tracking system. (A geometric correction factor would be applied in the case of other types of concentrating systems.) Once the average annual productivity for each system is determined, the next stage would be to perform an appropriate economic analysis utilizing the costs associated with each system. The simulation model, of course, does not have to be limited to the solar collector loop, but may also include other components of the overall system (such as the storage loop). 5. C O N C L U S I O N S The main conclusions from this analysis of the daily clearness index and radiation data in conjunction with the partition according to day type for Beer Sheva are the following: (1) This region is characterized by a relatively low percentage of cloudy days. Only for four months during the year does the monthly average percentage of cloudy days exceed 10%. Since the monthly average frequency of clear and partially cloudy days for Beer Sheva exceeds 80% throughout the year, this region is unequivocally amenable to the utilization of non-concentrating solar energy conversion systems. (2) There are no days classified as cloudy during the months of June through September and the monthly average percentage of clear days exceeds 50% during these months. Thus, the Beer Sheva region is a prime candidate for the use of solar energy conversion systems utilizing concentrating collectors due to its relatively high frequency of clear days and the fact that the monthly average daily values of the clearness index, even for partially cloudy days, are relatively high (KT > 0.50). (3) A general procedure has been outlined for utilizing the partition of days according to type analysis of the radiation data to analyze the relative merits of solar energy conversion by means of concentrating vis-fi-vis non-concentrating solar collector systems. Acknowledgements--We are indebted to E. Berman for partial support of this research by funding the purchase of the Normal IncidencePyrheliometersystem.We wish to thank G. Stanhillof the VolcaniInstitutefor remarks and suggestions during the preparation of this manuscript.We also wishto thank A. Manesand I. Seterof the Israel MeteorologicalService for their encouragementof this joint research project. REFERENCES
1. J. F. Orgill and K. G. T. Hollands, Sol. Energy 19, 357 (1977). 2. M. Iqbal, Sol. Energy 24, 491 (1980). 3. D. G. Erbs, S. A. Klein and J. A. Duffle,Sol. Energy 28, 293 (1982). 4. M. A. Chendo and A. A. L. Maduekwe,Sol. Energy 52, 247 (1994). 5. A. I. Kudish and A. Ianetz, Sol. Energy 48, 97 (1992). 6. World MeteorologicalOrganization, World Climate Program Report WCP-48 (1983). 7. A. Ianetz and A. I. Kudish, Energy 17, 523 (1992).